Low-mass-ratio (q) contact binary systems are progenitors of stellar mergers such as blue stragglers or fast-rotating FK Com stars. In this study, we present the first light curve analysis of two newly identified low mass-ratio contact binary systems, TIC 55007847 and TIC 63597006, that are identified from TESS. Both stars are classified as A-subtype contact binaries. We obtained the precise orbit periods for the two objects by using the O − C method, i.e., P = 0.6117108 day for TIC 55007847 and P = 0.7008995 day for TIC 63597006, and found an obvious periodic signal in the O − C curve of TIC 63597006. We suggest that the periodic signal comes from a third body. We further use the Markov chain Monte Carlo method with PHOEBE to derive the photometric solutions for the two binaries. The photometric solution for this object shows that the contribution of the third body is about 6%. Our analysis revealed that TIC 55007847 has an extremely low mass ratio of q = 0.08. By calculating the ratio of spin angular momentum to the orbital angular momentum J s/J o, we found that TIC 55007847 is very close to the instability threshold with J s/J o = 0.31, indicating that it may merge into a single, fast-rotating star in the future. For TIC 63597006, q = 0.14 and J s/J o = 0.15. This object is in a relatively stable evolutionary status at present.
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